Data

• The data used in this analysis was collected from WHO and United Nations website with the help of Deeksha Russell and Duan Wang. For more information about the data: https://www.kaggle.com/datasets/kumarajarshi/life-expectancy-who.
• Using observations from 2000 to 2015, the data compares the life expectancy for 193 countries based on certain factors like adult mortality, alcohol consumption, total expenditure e.t.c. The has a categorical variable called Status. Status tells us if the country is developed or developing.

Problem

• I am running a multiple linear regression analysis.
• My question is “Which factors make a bigger impact on the life expectancy age in developed and developing countries?”
  
• Using linear regression seems to be a good tool to decide if there is a strong correlation between certain factors and life expectancy.

My data has missing values, so my first step is to get rid of missing values. There is no further step needed to clean the original dataset.

A peek at the data:

datatable(head(life_df), extensions = 'FixedColumns',options = list(dom = 't',
                                scrollX = TRUE, fixedColumns = list(leftColumns = 3)))

Summary of each numeric variables variable in the data

sm = summary(life_df)
sm[1:6, c(2,4:12)]

##       Year      Life expectancy Adult Mortality infant deaths    
##  Min.   :2000   Min.   :44.0    Min.   :  1.0   Min.   :   0.00  
##  1st Qu.:2005   1st Qu.:64.4    1st Qu.: 77.0   1st Qu.:   1.00  
##  Median :2008   Median :71.7    Median :148.0   Median :   3.00  
##  Mean   :2008   Mean   :69.3    Mean   :168.2   Mean   :  32.55  
##  3rd Qu.:2011   3rd Qu.:75.0    3rd Qu.:227.0   3rd Qu.:  22.00  
##  Max.   :2015   Max.   :89.0    Max.   :723.0   Max.   :1600.00  
##     Alcohol       percentage expenditure  Hepatitis B       Measles      
##  Min.   : 0.010   Min.   :    0.00       Min.   : 2.00   Min.   :     0  
##  1st Qu.: 0.810   1st Qu.:   37.44       1st Qu.:74.00   1st Qu.:     0  
##  Median : 3.790   Median :  145.10       Median :89.00   Median :    15  
##  Mean   : 4.533   Mean   :  698.97       Mean   :79.22   Mean   :  2224  
##  3rd Qu.: 7.340   3rd Qu.:  509.39       3rd Qu.:96.00   3rd Qu.:   373  
##  Max.   :17.870   Max.   :18961.35       Max.   :99.00   Max.   :131441  
##       BMI        under-five deaths
##  Min.   : 2.00   Min.   :   0.00  
##  1st Qu.:19.50   1st Qu.:   1.00  
##  Median :43.70   Median :   4.00  
##  Mean   :38.13   Mean   :  44.22  
##  3rd Qu.:55.80   3rd Qu.:  29.00  
##  Max.   :77.10   Max.   :2100.00

sm[1:6, 13:22]

##      Polio       Total expenditure   Diphtheria       HIV/AIDS     
##  Min.   : 3.00   Min.   : 0.740    Min.   : 2.00   Min.   : 0.100  
##  1st Qu.:81.00   1st Qu.: 4.410    1st Qu.:82.00   1st Qu.: 0.100  
##  Median :93.00   Median : 5.840    Median :92.00   Median : 0.100  
##  Mean   :83.56   Mean   : 5.956    Mean   :84.16   Mean   : 1.984  
##  3rd Qu.:97.00   3rd Qu.: 7.470    3rd Qu.:97.00   3rd Qu.: 0.700  
##  Max.   :99.00   Max.   :14.390    Max.   :99.00   Max.   :50.600  
##       GDP              Population        thinness  1-19 years
##  Min.   :     1.68   Min.   :3.400e+01   Min.   : 0.100      
##  1st Qu.:   462.15   1st Qu.:1.919e+05   1st Qu.: 1.600      
##  Median :  1592.57   Median :1.420e+06   Median : 3.000      
##  Mean   :  5566.03   Mean   :1.465e+07   Mean   : 4.851      
##  3rd Qu.:  4718.51   3rd Qu.:7.659e+06   3rd Qu.: 7.100      
##  Max.   :119172.74   Max.   :1.294e+09   Max.   :27.200      
##  thinness 5-9 years Income composition of resources   Schooling    
##  Min.   : 0.100     Min.   :0.0000                  Min.   : 4.20  
##  1st Qu.: 1.700     1st Qu.:0.5090                  1st Qu.:10.30  
##  Median : 3.200     Median :0.6730                  Median :12.30  
##  Mean   : 4.908     Mean   :0.6316                  Mean   :12.12  
##  3rd Qu.: 7.100     3rd Qu.:0.7510                  3rd Qu.:14.00  
##  Max.   :28.200     Max.   :0.9360                  Max.   :20.70

There is a general trend for the average life expectancy age to be higher in developed countries than in developing countries.

This is the reason why I chose to evaluate predicting variables based on the status of the countries. What factors stand out the most?

life_dev = life_df %>% group_by(Status, Year) %>% 
  summarize(`Avg Life Expectancy` = round(mean(`Life expectancy`),1))

life_p = ggplotly(ggplot(life_dev, aes(x =Year, y = `Avg Life Expectancy`, fill = Status )) + 
            geom_bar(stat = "identity", position = position_dodge()) + 
            theme(axis.text.x= element_text(angle = 45,vjust = 0.5, hjust=1)) + 
            labs(title = "Average Expectancy Age per Year based on Status"))

life_p

The goal of this project is to find the factors that affect life expectancy in both developing and devloped countries. In order to achieve this, the data set has to be split into developing (undev_life) and developed (dev_life) sets.

undev_life = life_df %>% filter(Status == "Developing")
datatable(head(undev_life, 1), extensions = 'FixedColumns',options = list(dom = 't',
                                scrollX = TRUE, fixedColumns = list(leftColumns = 3)))

dev_life = life_df %>% filter(Status == "Developed")
datatable(head(dev_life, 1), extensions = 'FixedColumns',options = list(dom = 't',
                                scrollX = TRUE, fixedColumns = list(leftColumns = 3)))

Since there are multiple predictor variables, the following steps would be used to choose the best

• Step 1: Checking for multicollinearity using a correlation heat map
• Step 2: Eliminate Columns that cause multicollinearity
• Step 3: Apply multiple Linear regression model
• Step 4: Eliminating statistically insignificant factors based on p-value

Step 1: Checking for multicollinearity

undev_cor <-melt(round(cor(undev_life %>% select(`Life expectancy`:Schooling)), 2))

undev_corp <- ggplot(data =undev_cor, aes(x=Var1, y=Var2, fill=value)) + geom_tile() +
      geom_text(aes(Var2, Var1, label = value), color = "white", size = 2)+
      theme(axis.text.x = element_text(angle = 45, hjust = 1)) + 
      labs(title = "Correlation Heat Map (Developing)", x = "", y = "")

undev_corp

Step 2: Eliminate Columns that cause multicollinearity

To decide which columns cause multicollinearity, I checked for a |r| > 0.9. From the heat map the following cause multicollinearity:

1. Under five deaths and infant deaths
2. thinness 1-19 years and thinness 5 - 9 years
3. GDP and percentage expenditure

To decide which column to keep, I chose the column with highest |r| when compared to life expectancy Columns eliminated:

1. infant deaths
2. thinness 1-19 years
3. percentage expenditure

Step 3: Apply linear regression model

undev_m = lm(`Life expectancy`~`Adult Mortality`+`Alcohol`+`Hepatitis B` +`Measles`+`BMI` +
               `under-five deaths`+`Polio`+`Total expenditure`+`Diphtheria` +
               `HIV/AIDS`+`GDP`+`Population` + `thinness 5-9 years` +
               `Income composition of resources`+ `Schooling`, data = undev_life)

Step 4: Eliminating statistically insignificant factors based on p-value (alpha = 0.05)

datatable(summary(undev_m)$coefficients, options = list(pageLength = 8))

The columns eliminated: Hepatitis B, Polio, Total expenditure, Population, and thinness 5-9 years

The final regression is modeled using this:

Life Expectancy = Intercept+ Adult Mortality(x1) + Alcohol(x2) + Measles(x3) + BMI(x4) + under-five deaths(x5) + Diphtheria(x6) +HIV/AIDS(x7) + GDP(x8)+ Income composition of resources(x9) + Schooling(x10)

Step 1: Checking for multicollinearity among predictor variables

dev_cor <-melt(round(cor(dev_life %>% select(`Life expectancy`:Schooling)), 2))

dev_corp <- ggplot(data =dev_cor, aes(x=Var1, y=Var2, fill=value)) + geom_tile() +
        geom_text(aes(Var2, Var1, label = value), color = "white", size = 2)+
        theme(axis.text.x = element_text(angle = 45, hjust = 1)) + 
        labs(title = "Correlation Heat Map (Developed)", x = "", y = "")

dev_corp

## Warning: Removed 36 rows containing missing values (geom_text).

Step 2: Eliminate Columns that cause multicollinearity

To decide which columns cause multicollinearity, I checked for a |r| > 0.9. From the heat map the following cause multicollinearity:

1. Under five deaths and infant deaths
2. thinness 1-19 years and thinness 5 - 9 years
3. GDP and percentage expenditure

To decide which column to keep, I chose the column with highest |r| when compared to life expectancy Columns eliminated:

1. under-five deaths
2. thinness 5-9 years
3. percentage expenditure
4. HIV/AIDS (due to error “the standard deviation is zero”)

Step 3: Apply linear regression model

dev_m = lm(`Life expectancy`~`Adult Mortality`+`infant deaths`+`Alcohol`+ `Hepatitis B` +`Measles`+`BMI`+
 `Polio`+`Total expenditure`+`Diphtheria`+ `GDP`+`Population` + `thinness  1-19 years` +
   `Income composition of resources`+ `Schooling`, data = undev_life)

Step 4: Eliminating statistically insignificant factors based on p-value (alpha = 0.05)

datatable(summary(dev_m)$coefficients, options = list(pageLength = 8))

The columns eliminated: Hepatitis B, Total expenditure, Measles, Population, Polio, infant deaths

The final regression is modeled using this:

Life expectancy = Intercept + Adult Mortality(x1) + Alcohol(x2) +BMI(x3) + Diphtheria(x4) + GDP(x5) +thinness 1-19 years(x6) + Income composition of resources(x7)+ Schooling(x8)

Examining residual plots helps to see how effective my models are. Ideal residual plots should have a symmetrical distribution that clusters towards the middle of the plot.

My plot (on the next slide), does not fully conform to what an ideal residual plots is supposed to look like.

Creeating Subplots

undev_p = plot_ly(x=undev_m1$fitted.values, y=undev_m1$residuals, type="scatter", mode="markers",
                name = "developing", marker = list(color = "blue")) 

dev_p = plot_ly(x = dev_m1$fitted.values, y = dev_m1$residuals, type = "scatter", mode= "markers",
                name = "developed", marker = list(color = "red"))

plots <- subplot(undev_p, dev_p, nrows = 2) %>% layout(title = "Residuals vs Fitted Values", 
                yaxis = list(title = "Residuals"), xaxis = list(title = "Fitted Values"), 
                margin = list(l = 50, r = 1, b = 1, t = 80))
plots

According to regression models the factors affecting life expectancy in developing countries include:- Adult Mortality, Alcohol, Measles, BMI, under-five deaths, Diphtheria, HIV/AIDS, GDP, Income composition of resources, Schooling

Factors affecting life expectancy in developed countries include:- Adult Mortality, Alcohol, BMI, Diphtheria, GDP, thinness 1-19 years, Income composition of resources, Schooling.

Factors that cut across both models include:- Adult Mortality, Alcohol, BMI, Diphtheria, GDP, Income composition of resources, Schooling.

Although, looking at my residual plots, I have an unbalanced Y-axis, which means my models could be made significantly more accurate.

(Presentation link: https://asu.zoom.us/rec/share/TJk2uFoqU9Jy67QiUhFYLTDvypuUge5HcczaTLnu66jxKkXjKsKMh-AJoiToyLe5.t8nmhdg478nqFVB_

Access Passcode: dat301_Project1)